In this talk,two conservative difference schemes,i.e.,the Crank-Nicolson difference scheme and the linearly conservative difference scheme for the coupled nonlinear Schrodinger equations with space fractional derivative are proposed.The existence and uniqueness of the difference solutions of the two schemes are proved.The stability and convergence of the schemes are discussed,and they are shown to be convergent of order O( 2 + h2) in l2 norm with the time step and mesh size h.When the fractional order is two,all those results are in accord with the difference schemes proposed for the classical non-fractional coupled nonlinear Schrodinger equations.Some numerical examples are also reported.